The Central Limit Theorem states that when the sample size is large enough, the sampling distribution approximates a normal distribution regardless of the shape of the population distribution.
This theorem is useful because you can make inferences about the population parameter without knowing the population size.
As a rule of thumb, a sample size of 30 or greater is often required for the central limit theorem to be applicable.
The maximum sample size of a given population is 10% of the population or 1000 (whichever is lower)
To find the sample mean and standard deviation, you need to provide the population mean (μ), the population standard deviation (σ), and the sample size (n):
Sample mean (x̅): 18.00000
Sample std. deviation (s): 0.54772
The sample mean (x̅) would be equal to the population mean (μ) when the sample size is large enough.
The standard deviation (s) is calculated as follows:
s = σ / √n
The calculator above should help you find the values quickly. Happy analyzing!
